5 citations · 8 across the 5 of their papers we have counts for
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Galois Theory, discriminants and torsion subgroups of elliptic curves
Irene Garcia-Selfa, Enrique Gonzalez-Jimenez, Jose M. Tornero
We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown…
On the discriminant of elliptic curves with non-trivial torsion
I. Garcia-Selfa, Jose M. Tornero
For those elliptic curves defined over the rational with non--trivial torsion subgroup, we find a tight relationship between the torsion subgroup itself and a Galois group naturall…
Thue equations and torsion groups of elliptic curves
Irene Garcia-Selfa, Jose M. Tornero
A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equation…
Searching for simultaneous arithmetic progressions on elliptic curves
Irene Garcia-Selfa, Jose M. Tornero
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is…
A complete diophantine characterization of the rational torsion of an elliptic curve
Irene Garcia-Selfa, Jose M. Tornero
We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non-)existence of integral solutions of a system of diophantine equations.
On simultaneous arithmetic progressions on elliptic curves
I. Garcia-Selfa, J. M. Tornero
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results…